Radiative Dirac Neutrino Masses from Modular $S_3$ Symmetry in an Axion Model

We present a unified axion model framework that simultaneously addresses the origin of neutrino masses, leptonic flavor structure, the strong CP problem, and dark matter. The model is based on a global $U(1{)}_{\mathrm{P}\mathrm{Q}}$ symmetry combined with a modular $S_3$ symmetry and is realized within a novel class of KSVZ-type axion model. Exotic colored fermions and scalars mediate radiative neutrino mass generation at the one loop-level. The PQ charge assignment forbids tree-level neutrino masses and leaves a residual $Z_3$ symmetry that ensures the Dirac nature of neutrinos. In the minimal realization, the neutrino mass matrix is of rank two, predicting one massless neutrino. Consequently, the sum of neutrino masses is constrained for both the normal and inverted hierarchies. We analyze the implications for charged lepton flavor violation and the lepton $g-2$. The axion emerging from this framework dynamically resolves the strong CP problem and accounts for the observed dark matter abundance. Notably, the predicted axion-photon coupling is within reach of upcoming experiments and consistent with existing astrophysical and cosmological bounds.